import holoviews as hv
import holoviews.operation as op
import numpy as np
import holoviews.plotting.hooks
%load_ext holoviews.ipython
%output backend='d3' size=100 dpi=150

wtp = np.arange(0.1, 0.6, 0.05)
steepness_of_income_drop = np.arange(0.6, 1, 0.05)
current_interest_rates = np.arange(0, 0.75, 0.05)
num_houses = range(2,10)

wtp = [0.4, 0.5, 0.6, 0.7]
steepness_of_income_drop = [0.6, 0.7, 0.8]
current_interest_rates =[.02, 0.03, 0.05]
num_houses = [1, 4, 6, 8]

keys = []
for w in wtp:
    for s in steepness_of_income_drop:
        for c in current_interest_rates:
            for n in num_houses:
                keys.append((w,s,c,n))
minimum_house_cost = 1e5
median_income = 65e3

def make_incomes(median, steepness_of_income_drop):
    """
    This function will generate a distribution of incomes in an inequal society. We set the
    median, and every person earns only a proportion of the previous persons income.
    
    :param median: Median income of the group
    :param steepness_of_income_drop: A float in the range (0, 1), a number close to 0 is
                                     a very inequal society, a number close to 1 is a very
                                     equal society.
    
    :returns: A list of incomes of length 9.
    """
    bottom_4 = []
    prev = median
    for i in range(4):
        bottom_4.append(prev*steepness_of_income_drop)
        prev = bottom_4[-1]
    top_4 = []
    prev = median
    for i in range(4):
        top_4.append(prev/steepness_of_income_drop)
        prev = top_4[-1]
    incomes = bottom_4
    incomes.extend(top_4)
    incomes.append(median)
    incomes = np.sort(incomes)
    return incomes

def add_x_index(y):
    """
    Adds an X index in a manner suitable for holoviews Curve element.
    
    
    :params y: vector to be appended
    :returns: a list of lists of length two, representing coordinates.
    """
    y = y.tolist()
    return zip(range(len(y)), y)

def calculate_house_cost(incomes, minimum_house_cost, num_houses, interest_rate, wtp):
    """
    If there are an equal number of houses and people, then the house costs whatever the 
    marginal cost is for a house. If there are not enough houses then the price of the house
    is $1 more than the poorest person is willing to pay.
    
    :param incoms: A list of incomes for each buyer.
    :param minimum_house_cost: The minimum cost to build a house.
    :param interest_rate: The current interest rate
    :param wtp: The willingness to pay (for everyone) as a proportion of their income (0-1)
    
    :returns: A list of house prices for each person. $0 if a person does not buy a house.
    """
    house_cost = np.zeros(len(incomes))
    if num_houses >= len(incomes):
        house_cost = np.ones(len(incomes)) * minimum_house_cost
        return house_cost
    else:
        # Now we have to bargain.
        # calculate each person's willingness to pay (absolute value)
        WTP = np.array(incomes) * np.array(wtp)
        # Now, calculate how much they could borrow given that. 
        WTP = WTP/interest_rate # represents the max that they could borrow to buy the house.
        # Now assume that they require (and can access at 15% deposit)
        WTP = WTP / 0.85
        
        winners = np.argsort(WTP)
        WTP = np.sort(WTP)
        
        # The new house price is equal to the value that the person who misses out plus 1.
        
        house_cost = (WTP[len(incomes) - num_houses] + 1)*np.ones(len(incomes))/1e3
        house_cost[0:len(incomes)-num_houses] = 0
        return  zip(range(len(incomes)), house_cost)


res = calculate_house_cost(make_incomes(median_income, 0.7), 1e5, 5, 0.5, 0.70)

# Build holo-views data.
d1 = {k: hv.Scatter(calculate_house_cost(make_incomes(median_income, k[1]), minimum_house_cost, k[3], k[2], k[0]),
                key_dimensions=['house location'], value_dimensions=['House Price (\'000)'])                  
                  for k in keys }
d2 = {k[1]: hv.Curve(add_x_index(make_incomes(median_income, k[1])))  for k in keys }

h1 = hv.HoloMap(d1, key_dimensions = ['wtp', 'income_drop', 'interest_rate', 'num_houses'])
h2 = hv.HoloMap(d2, key_dimensions=[ 'income_drop'])

%%opts Layout [figure_size=100 figure_bounds=(0.1,0,1,1)] 
# Generate holoview plots
h1+h2